ArticleOriginal scientific text

Title

Charge transfer scattering in a constant electric field

Authors 1

Affiliations

  1. Institut de Mathématiques de Paris-Jussieu, UMR 9994, Université Paris 7 (D. Diderot), 2 Place Jussieu, 75252 Paris Cedex 05, France

Abstract

We prove the asymptotic completeness of the quantum scattering for a Stark Hamiltonian with a time dependent interaction potential, created by N classical particles moving in a constant electric field.

Bibliography

  1. T. Adachi and H. Tamura, Asymptotic completeness for long range many-particle systems with Stark effect, J. Math. Sci. Univ. Tokyo 2 (1995), 77-116.
  2. T. Adachi and H. Tamura, Asymptotic completeness for long range many-particle systems with Stark effect. II, Comm. Math. Phys. 174 (1996), 537-559.
  3. W. O. Amrein, A. Boutet de Monvel and V. Georgescu, Lp-inequalities for the Laplacian and unique continuation, Ann. Inst. Fourier (Grenoble) 31 (1981), no. 3, 153-168.
  4. W. O. Amrein, A. Boutet de Monvel and V. Georgescu, C0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians, Birkhäuser, 1996.
  5. J. E. Avron and I. W. Herbst, Spectral and scattering theory for Schrödinger operators related to Stark effect, Comm. Math. Phys. 52 (1977), 239-254.
  6. J. Dereziński and C. Gérard, Asymptotic Completeness of N-Particle Systems, Springer, 1996.
  7. G. M. Graf, Phase space analysis of the charge transfer model, Helv. Phys. Acta 63 (1990), 107-138.
  8. G. M. Graf, Asymptotic completeness for N-body short-range quantum systems: a new proof, Comm. Math. Phys. 123 (1990), 107-138.
  9. G. M. Graf, A remark on long-range Stark scattering, Helv. Phys. Acta 64 (1991), 1167-1174.
  10. G. A. Hagedorn, Asymptotic completeness for the impact parameter approximation to the three particle scattering, Ann. Inst. H. Poincaré, Sect. A 36 (1982), 19-40.
  11. B. Helffer et J. Sjöstrand, Equation de Schrödinger avec champ magnétique et équation de Harper, in: Lecture Notes in Phys. 345, Springer, 1989, 118-197.
  12. I. W. Herbst, Unitary equivalence of Stark effect Hamiltonians, Math. Z. 155 (1977), 55-70.
  13. I. W. Herbst, J. S. Mοller and E. Skibsted, Spectral analysis of N-body Stark Hamiltonians, Comm. Math. Phys. 174 (1995), 261-294.
  14. I. W. Herbst, J. S. Mοller and E. Skibsted, Asymptotic completeness for N-body Stark Hamiltonians, ibid. 174 (1996), 509-535.
  15. A. Jensen, Scattering theory for Stark Hamiltonians, Proc. Indian Acad. Sci. (Math. Sci.) 104 (1994), 599-651.
  16. A. Jensen and T. Ozawa, Existence and non-existence results for wave operators for perturbations of the Laplacian, Rev. Math. Phys. 5 (1993), 601-629.
  17. A. Jensen and K. Yajima, On the long range scattering for Stark Hamiltonians, J. Reine Angew. Math. 420 (1991), 179-193.
  18. E. L. Korotyaev, On the scattering theory of several particles in an external electric field, Math. USSR-Sb. 60 (1988), 177-196.
  19. P. A. Perry, Scattering Theory by the Enss Method, Math. Rep. 1, Harwood, 1983, 1-347.
  20. I. M. Sigal, Stark effect in multielectron systems: non-existence of bound states, Comm. Math. Phys. 122 (1989), 1-22.
  21. I. M. Sigal and A. Soffer, The N-particle scattering problem: asymptotic completeness for the short-range quantum systems, Ann. of Math. 125 (1987), 35-108.
  22. H. Tamura, Scattering theory for N-particle systems with Stark effect: asymptotic completeness, RIMS Kyoto Univ. 29 (1993), 869-884.
  23. D. A. White, The Stark effect and long-range scattering in two Hilbert spaces, Indiana Univ. Math. J. 39 (1990), 517-546.
  24. D. A. White, Modified wave operators and Stark Hamiltonians, Duke Math. J. 68 (1992), 83-100.
  25. U. Wüller, Geometric methods in scattering theory of the charge transfer model, ibid. 62 (1991), 273-313.
  26. K. Yajima, A multi-channel scattering theory for some time dependent hamiltonians, Charge Transfer Problem, Comm. Math. Phys. 75 (1980), 153-178.
  27. K. Yajima, Spectral and scattering theory for Schrödinger operators with Stark effect, J. Fac. Sci. Univ. Tokyo Sect. IA 26 (1979), 377-390.
  28. K. Yajima, Spectral and scattering theory for Schrödinger operators with Stark effect, II, ibid. 28 (1981), 1-15.
  29. L. Zieliński, Complétude asymptotique pour un modèle du transfert de charge, Ann. Inst. H. Poincaré Phys. Théor. 58 (1993), 363-411.
  30. L. Zieliński, Scattering for a dispersive charge transfer model, ibid. 65 (1997), 339-386.
  31. L. Zieliński, Asymptotic completeness for multiparticle dispersive charge transfer model, J. Funct. Anal. 150 (1997), 453-470.
  32. L. Zieliński, Dispersive charge transfer model with long range interactions, J. Math. Anal. Appl. 217 (1998), 43-71.
  33. J. Zorbas, Scattering theory for Stark Hamiltonians involving long range potentials, J. Math. Phys. 19 (1978), 577-580.
Pages:
37-61
Main language of publication
English
Received
1997-03-17
Accepted
1998-05-12
Published
1999
Exact and natural sciences